IMO Practice Test — Algebraic Expressions (Two-step)
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
Simplify: 3(2x + 4) - 2(x - 3)
4x + 18
4x + 6
8x + 6
8x + 18
Explanation: 6x + 12 - 2x + 6 = 4x + 18
Question 2 of 6
hard
Factor completely: 12x^2 - 18x
6x(2x - 3)
6(2x^2 - 3x)
3x(4x - 6)
2x(6x - 9)
Explanation: GCF = 6x. So 12x^2 - 18x = 6x(2x - 3).
Question 3 of 6
hard
The perimeter of a rectangle is 8x + 12. If the width is x + 2, find the length.
3x + 4
3x + 2
4x + 3
2x + 4
Explanation: Perimeter = 2(L+W). 2(L+x+2)=8x+12. 2L+2x+4=8x+12. 2L=6x+8. L=3x+4.
Question 4 of 6
hard
Simplify: 5a - [3b - {2a - (b - a)}]
2a - 4b
2a - 2b
8a - 4b
8a - 2b
Explanation: Innermost: b-a. Then 2a-(b-a)=3a-b. Then 3b-(3a-b)=4b-3a. Then 5a-(4b-3a)=8a-4b.
Question 5 of 6
hard
If (x+y)/2 = x + 5 and x = 4, find y.
y = 14
y = 10
y = 8
y = 6
Explanation: (4+y)/2 = 4+5 = 9. So 4+y = 18. Therefore y = 14.
Question 6 of 6
hard
The expression ax + 2x + 3a + 6 can be factored as (x+3)(a+2). For which value of a is this an identity?
Any real number
a = 2
a = 3
No solution
Explanation: Expanding (x+3)(a+2) gives ax+2x+3a+6 — this is true for all values of a, so it is an identity.